Problem: Is ${412260}$ divisible by $4$ ?
Explanation: A number is divisible by $4$ if the last two digits are divisible by $4$ . [ Why? We can rewrite the number as a multiple of $100$ plus the last two digits: $ \gray{4122} {60} = \gray{4122} \gray{00} + {60} $ Because $412200$ is a multiple of $100$ , it is also a multiple of $4$ So as long as the value of the last two digits, ${60}$ , is divisible by $4$ , the original number must also be divisible by $4$ Is the value of the last two digits, $60$ , divisible by $4$ Yes, ${60 \div 4 = 15}$, so $412260$ must also be divisible by $4$.